A copper wire has a diameter "d" is heated by a short circuit to "T_0" before a slow-blow fuse burns out. If the still air temperature is "T_a", how long will it take for the wire to drop to temperature "T", if the variable τ (tau) is found to be 0.02 hr ?
The following material properties are given:
k = 224 (BTU-ft/hr-ft2 -o R)
h = 1.65 (BTU/hr-ft2 -o R)
cp = 0.091 (BTU/lbm-o R)
rho = 558 (lbm/ft3 )
T_a = 99F
T = 139F
T_0 = 296F

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.